Toward an efficient algorithm for deciding the vanishing of local cohomology modules in prime characteristic

2014/07/09 by Yi Zhang, Zhang, Yi
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Algebraic Geometry and Number Theory #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1407.2583

Abstract

Let R=k[x₁,…,x_n] be a ring of polynomials over a field k of characteristic p>0. There is an algorithm due to Lyubeznik for deciding the vanishing of local cohomology modules Hⁱ_I(R) where I⊂ R is an ideal. This algorithm has not been implemented because its complexity grows very rapidly with the growth of p which makes it impractical. In this paper we produce a modification of this algorithm that consumes a modest amount of memory.

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